On Generalized Fibonacci And Lucas Numbers By Matrix Methods

Gamaliel Cerda-morales

On Generalized Fibonacci And Lucas Numbers By Matrix Methods

Year 2013, Volume: 42 Issue: 2, 173 - 179, 01.02.2013

Abstract

In this study we define the generalized Lucas V (p, q)-matrix similar tothe generalized Fibonacci U (1, −1)-matrix. The V (p, q)-matrix is different from the Fibonacci U (p, q)-matrix, but is related to it. Using thismatrix representation, we have found some well-known equalities anda Binet-like formula for the generalized Fibonacci and Lucas numbers.

Keywords

Matrix methods, generalized Lucas numbers, Binet’s formula.

References

Gould, H.W.,A history of the Fibonacci Q-matrix and a higher-dimensional problem, Fibonacci Quart. 19, 7-250, 1981.
Horadam, A. F., Jacobsthal representation numbers, Fibonacci Quarterly, 34, 40-54, 1996. Kalman, D. and Mena, R., The Fibonacci numbers - exposed, Math. Mag., 76, 81-167, 2003. Koshy, T.,Fibonacci and Lucas Numbers with Applications, Wiley - Interscience, New York, 200
Silvester, J.R.,Fibonacci properties by matrix methods, Mathematical Gazette 63, 188-191, 197

On Generalized Fibonacci And Lucas Numbers By Matrix Methods

Year 2013, Volume: 42 Issue: 2, 173 - 179, 01.02.2013

Gamaliel Cerda-morales

Abstract

-

Keywords

-

References

Gould, H.W.,A history of the Fibonacci Q-matrix and a higher-dimensional problem, Fibonacci Quart. 19, 7-250, 1981.
Horadam, A. F., Jacobsthal representation numbers, Fibonacci Quarterly, 34, 40-54, 1996. Kalman, D. and Mena, R., The Fibonacci numbers - exposed, Math. Mag., 76, 81-167, 2003. Koshy, T.,Fibonacci and Lucas Numbers with Applications, Wiley - Interscience, New York, 200
Silvester, J.R.,Fibonacci properties by matrix methods, Mathematical Gazette 63, 188-191, 197

There are 3 citations in total.

Details

Primary Language	Turkish
Journal Section	Mathematics
Authors	Gamaliel Cerda-morales
Publication Date	February 1, 2013
Published in Issue	Year 2013 Volume: 42 Issue: 2

Cite

APA	Cerda-morales, G. (2013). On Generalized Fibonacci And Lucas Numbers By Matrix Methods. Hacettepe Journal of Mathematics and Statistics, 42(2), 173-179.
AMA	Cerda-morales G. On Generalized Fibonacci And Lucas Numbers By Matrix Methods. Hacettepe Journal of Mathematics and Statistics. February 2013;42(2):173-179.
Chicago	Cerda-morales, Gamaliel. “On Generalized Fibonacci And Lucas Numbers By Matrix Methods”. Hacettepe Journal of Mathematics and Statistics 42, no. 2 (February 2013): 173-79.
EndNote	Cerda-morales G (February 1, 2013) On Generalized Fibonacci And Lucas Numbers By Matrix Methods. Hacettepe Journal of Mathematics and Statistics 42 2 173–179.
IEEE	G. Cerda-morales, “On Generalized Fibonacci And Lucas Numbers By Matrix Methods”, Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 2, pp. 173–179, 2013.
ISNAD	Cerda-morales, Gamaliel. “On Generalized Fibonacci And Lucas Numbers By Matrix Methods”. Hacettepe Journal of Mathematics and Statistics 42/2 (February 2013), 173-179.
JAMA	Cerda-morales G. On Generalized Fibonacci And Lucas Numbers By Matrix Methods. Hacettepe Journal of Mathematics and Statistics. 2013;42:173–179.
MLA	Cerda-morales, Gamaliel. “On Generalized Fibonacci And Lucas Numbers By Matrix Methods”. Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 2, 2013, pp. 173-9.
Vancouver	Cerda-morales G. On Generalized Fibonacci And Lucas Numbers By Matrix Methods. Hacettepe Journal of Mathematics and Statistics. 2013;42(2):173-9.